No, universities are not operating more like businesses. They are operating more like farmers of tax money.
A business will seek to provide a good or service that its customers want. A good business will seek to provide a good or service that its customers want, and that is also good for them. Current universities are doing something very different.
Consider the thesis of this book.
The Economic Laws of Scientific Research
His claim (backed up with huge swathes of data and analysis) is this. If you get government out of the business of education, universities will end up with more money, and less restraints. Yes yes, the crowd here that think you can only get money from government grants is outraged.
Outrage is not an argument. Let me explain the book.
Consider Fred's Transistor Company (FTC). They want some research done on some new semi-conductor. But they don't want to buy their own labs. So they go to the local physics department and ask them. And FTC has to find out what motivates professors.
And that comes under the heading "academic freedom." Part of that is money, but by no means all. It has aspects such as the right to publish your work, the right to read other people's work, the right to have or be a visiting speaker or researcher. The right to get some post-docs in, or research associates. The right to visit some place with special resources or facilities. Like special labs or libraries or archives or research sites, etc. And the right to have a comfortable university with various facilities like poetry readings and art and music and philosophy discussions, and so on. And a good library on campus. And so on and so forth, all the things that make up a university life, which would require many thousands of words to cover even a small fraction.
So FTC negotiates with the physics department. And the science faculty. And the various powers-that-be at the university. And they drop a stack of cash on the physics department, and another stack on the university leadership.
The only restraint is, they want time to make commercial use of the research before it is published in full. After that, they literally do not care what the university does with the money. They can give it to whatever part or portion of the university, for whatever purpose, the university cares to apply. University related funding decisions made internally to the university.
Consider this applied across the uni. This company wants some research on its new thing to keep birds out of airplane flight paths and maybe out of wind turbines. This company wants to know if this chemical is safe to put in toothpaste. And so on, and so forth. They would all like to get their research done without having to buy their own labs.
Then consider the area of specialty training. This company needs its staff to learn French to do business in Canada. This company needs some staff to learn to recognize artifacts of various types because they deal in antiquities. This company needs staff trained in how to write an environmental report. This company needs staff trained in how to use the latest equipment in forestry. And so on.
What is the result? Each $2 of government money the university gets removes $3 of private money. And, government money comes with huge sheaves of restraints and restrictions and regulations and paper work and promises and constraints. From "give your research to this three-letter-agency for nothing" to "hire this guy we say needs a job" to "charge students this much tuition, no more or less" to "you can only do this kind of research or no grant for you" to "you must have this many books in your library, this big a sports center, this many faculty-to-students" and so on and so on.
What is the result of taking government money? The need for ever more administrators to deal with the constraints placed by government money. And far less money than private grants would have provided.
Why would a university operate this way? It is clearly bad for students, bad for profs, bad for research, and bad for society at large.
It is good for administrators. And the admin run the unies.
"Pournelle's iron law of bureaucracy" tells us why that is happening.
In any bureaucracy, the people devoted to the benefit of the bureaucracy itself always get in control and those dedicated to the goals the bureaucracy is supposed to accomplish have less and less influence, and sometimes are eliminated entirely..
Universities are not operating as businesses. They are operating as cronies of various government agencies and politicians. Admin and government feed and help each other. Governments insist only universities can prepare people for a career, then they prop up the price, then they provide subsidies to pay for the inflated price. Then the admin squashes any dissent within the university, and scares off any private money that might somehow make it in the door. As I mentioned in a comment under another answer, tuition has doubled in ten years. Classes are still full. And grants have gone up 50%. Yet the universities cry poor. That's because steadily more-and-more of the incoming cash is used to feed the admin
and satisfy the government-imposed constraints.
A final quote from the cite behind that word admin
Figure 3 clearly shows a rather steep decrease in the number of students per administrator over the past 15 years in both SAIS and NAIS schools. For NAIS schools, there were 41.1 students for every administrator in 2001-2002. By 2016-2017, the number of students per administrator lowered to 27. This represents a 53% difference. For SAIS schools, the number of students per administrator was 59 in 2001-2002, by 2016-2017 the number dropped to 39. This represents a 60% difference.
Universities have become places where administrators spend tax money and government subsidized tuition money. They are by no means businesses. They are barely still universities.
Note added to respond to comments: Why would FTC fund stuff not related to their transistor? I already explained that. They pay the uni for the right to work with the physics department. Or the biology department if it's biology research, or the engineering department if it's engineering research. Or the languages faculty if it's specialty language training. And so on.
So if you are worried that you couldn't get funding from your uni, even if your uni had 50 percent more money, then you are admitting your fellow professors don't evaluate your work as worth funding.